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中学阶段所要解的不等式,除有理不等式外,还有无理不等式,指数、对数不等式等。解法一般是根据具体情况,写出同解组,归结为解有理不等式。但我们也可以根据初等函数在它们的定义区间上是连续的;在区间(α,b)上连续的函数,函数值在(α,b)上处处不为零,那么在(α,b)上函数值有相同的符号。将各种不等式统一分三步求解。下面通过解不等式 (3x+7)~(1/2)-x-1>0,(1)来详细说明方法: 解:1)求定义域(使不等式两端都有意义的文字x的取值集合)易见为:x≥-7/3 。把定义域在数轴上表示出来。 2)解对应方程:(3x+7)~(1/2)-x-1=0,得x_1=3,x_2=-2,经
In addition to the rational inequalities, the inequalities to be solved in the secondary school stage include unreasonable inequalities, indices, logarithmic inequalities, and so on. The solution is generally based on the specific circumstances, write the same solution group, boiled down to solve the rational inequality. However, we can also use the elementary functions to be continuous in their defined intervals; in the interval (α,b), continuous functions whose function values are not zero everywhere in (α,b), then in (α,b) The upper function value has the same sign. The various inequalities are unanimously divided into three steps. The following is a detailed description of the method by solving the inequality (3x+7)~(1/2)-x-1>0,(1): Solution: 1) Find the definition field (make the text x that makes sense on both ends of the inequality) The set of values) is easily seen as: x≥-7/3. The domain is represented on the axis. 2) Solve the corresponding equation: (3x+7)~(1/2)-x-1=0, get x_1=3, x_2=-2,